Terrestrial Sapajus

Creating a Grid and Visualizing Data

## Warning: st_centroid assumes attributes are constant over geometries

## Warning in min(x): no non-missing arguments to min; returning Inf

## Warning in max(x): no non-missing arguments to max; returning -Inf

## Warning in validateCoords(lng, lat, funcName): Data contains 1 rows with either
## missing or invalid lat/lon values and will be ignored

## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries

Visualize Raw Data

Below are mapview interactive maps of raw data

mapview(grid_110m , alpha.regions = 0.2, alpha = 1 , col.regions="darkgrey" ) + mapview(grid_22m , alpha.regions = 0.2, alpha = 1 , col.regions="grey") + mapview(focals_data_cropped , cex=2, zcol="nutcrackin") +  mapview(nutcracking_data_cropped, col.regions ="violet", cex=2 ) + mapview(palm_trees, col.regions = "green3", cex=2)

mapview(focals_data_cropped , cex=2, zcol="individual")

grid_110m

## Simple feature collection with 1000 features and 9 fields
## Geometry type: POLYGON
## Dimension:     XY
## Bounding box:  xmin: 288756.2 ymin: 9576576 xmax: 290076.2 ymax: 9577126
## Projected CRS: WGS 84 / UTM zone 24S
## First 10 features:
##    grid_id id     left     top    right  bottom cell_id count_palm_trees
## 1        1  1 289966.2 9576906 290076.2 9576796     483                0
## 2        1  1 289966.2 9576906 290076.2 9576796     601                0
## 3        1  1 289966.2 9576906 290076.2 9576796     482                2
## 4        1  1 289966.2 9576906 290076.2 9576796     484                0
## 5        1  1 289966.2 9576906 290076.2 9576796     602                0
## 6        1  1 289966.2 9576906 290076.2 9576796     603                0
## 7        1  1 289966.2 9576906 290076.2 9576796     604                0
## 8        1  1 289966.2 9576906 290076.2 9576796     542                1
## 9        1  1 289966.2 9576906 290076.2 9576796     543                0
## 10       1  1 289966.2 9576906 290076.2 9576796     544                0
##    rawstones_average                       geometry
## 1               1.33 POLYGON ((289966.2 9576906,...
## 2               1.33 POLYGON ((289966.2 9576906,...
## 3               1.33 POLYGON ((289966.2 9576906,...
## 4               1.33 POLYGON ((289966.2 9576906,...
## 5               1.33 POLYGON ((289966.2 9576906,...
## 6               1.33 POLYGON ((289966.2 9576906,...
## 7               1.33 POLYGON ((289966.2 9576906,...
## 8               1.33 POLYGON ((289966.2 9576906,...
## 9               1.33 POLYGON ((289966.2 9576906,...
## 10              1.33 POLYGON ((289966.2 9576906,...

mynewspdf <- merge(grid_110m,average_stones_plot, duplicateGeoms = T)

1. Do monkeys use tools more frequently in areas where they go more to the ground outside tool use context?

• terrest (out of context)
• palm density
• stone availability
• rio? but not direct, for prediction not causal

For this, I will one model out of many I ran, that is the most complete and drives home the gist. This gives similar results to one that accounts for the length of follow (i.e. 1 to 5 minutes), but we can wait till the the actual tool use rates per follow are calculated. Essentially, this is a logistic GLMM that models the probability of using tools in a follow as predicted by empirical palm tree density in the 22m cell where the follow started (double check), the posterior density of mean stone density in the corresponding 110m cell, and an interaction between the 2.

We estimated varying intercepts and slopes for all parameters for each individual capuchin. Stone density was models as a Poisson GLMM with a log link, where we estimated a unique varying intercept for each 110m grid cell. This estimate (or a centered version of it) gets passed to the main GLMM, so we can use the distribution of stones to inform the mean, rather than a single, overconfident point estimate.

set.seed(345)
m10me <- ulam(
  alist(
    #stone model
    stone_raw_grid ~ dpois( lambda ), #define poisson likelihood
    log(lambda) <-  a_bar + a_grid[stone_grid_index],
    #priors
    a_bar ~ dnorm( 3 , 2 ), #mean effect on logscale
    a_grid[stone_grid_index] ~ dnorm( 0 , sigma_stone ), #priovarying effects centered on mean
    sigma_stone ~ dexp(1), #p
    #nutcracking model
    nutcrackin ~ dbinom(1, p ),
    logit(p) <-ap + a_id[id,1] +  (bS + a_id[id,2])*a_grid[grid_id_follow] +
      (bPT + a_id[id,3])*count_palm_std + (bPTxS + a_id[id,4])*a_grid[grid_id_follow]*count_palm_std,
    # adaptive priors - non-centered
    transpars> matrix[id,4]:a_id <-
      compose_noncentered( sigma_id , L_Rho_id , z_id ),
    matrix[4,id]:z_id ~ normal( 0 , 1 ),
    # fixed priors
    c(ap,bS,bPT,bPTxS) ~ dnorm( 0 , 1 ),
    vector[4]:sigma_id ~ dexp(1),
    cholesky_factor_corr[4]:L_Rho_id ~ lkj_corr_cholesky( 3 ),
    # compute ordinary correlation matrixes from Cholesky factors
    gq> matrix[4,4]:Rho_id <<- Chol_to_Corr(L_Rho_id)
    
  ) , data=data_list_daily , chains=4 , cores=4, log_lik=FALSE, iter=4000, pars_omit = 'z_id' , control=list(adapt_delta=0.99))

## Running MCMC with 4 parallel chains, with 1 thread(s) per chain...
## 
## Chain 1 Iteration:    1 / 4000 [  0%]  (Warmup)

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 2 Iteration:    1 / 4000 [  0%]  (Warmup)

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 3 Iteration:    1 / 4000 [  0%]  (Warmup)

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 4 Iteration:    1 / 4000 [  0%]  (Warmup)

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[3] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f547f39a7f8.stan', line 36, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 2 Iteration:  100 / 4000 [  2%]  (Warmup) 
## Chain 3 Iteration:  100 / 4000 [  2%]  (Warmup) 
## Chain 1 Iteration:  100 / 4000 [  2%]  (Warmup) 
## Chain 4 Iteration:  100 / 4000 [  2%]  (Warmup) 
## Chain 3 Iteration:  200 / 4000 [  5%]  (Warmup) 
## Chain 2 Iteration:  200 / 4000 [  5%]  (Warmup) 
## Chain 3 Iteration:  300 / 4000 [  7%]  (Warmup) 
## Chain 4 Iteration:  200 / 4000 [  5%]  (Warmup) 
## Chain 1 Iteration:  200 / 4000 [  5%]  (Warmup) 
## Chain 2 Iteration:  300 / 4000 [  7%]  (Warmup) 
## Chain 3 Iteration:  400 / 4000 [ 10%]  (Warmup) 
## Chain 4 Iteration:  300 / 4000 [  7%]  (Warmup) 
## Chain 3 Iteration:  500 / 4000 [ 12%]  (Warmup) 
## Chain 2 Iteration:  400 / 4000 [ 10%]  (Warmup) 
## Chain 4 Iteration:  400 / 4000 [ 10%]  (Warmup) 
## Chain 3 Iteration:  600 / 4000 [ 15%]  (Warmup) 
## Chain 1 Iteration:  300 / 4000 [  7%]  (Warmup) 
## Chain 3 Iteration:  700 / 4000 [ 17%]  (Warmup) 
## Chain 2 Iteration:  500 / 4000 [ 12%]  (Warmup) 
## Chain 4 Iteration:  500 / 4000 [ 12%]  (Warmup) 
## Chain 1 Iteration:  400 / 4000 [ 10%]  (Warmup) 
## Chain 4 Iteration:  600 / 4000 [ 15%]  (Warmup) 
## Chain 2 Iteration:  600 / 4000 [ 15%]  (Warmup) 
## Chain 3 Iteration:  800 / 4000 [ 20%]  (Warmup) 
## Chain 4 Iteration:  700 / 4000 [ 17%]  (Warmup) 
## Chain 2 Iteration:  700 / 4000 [ 17%]  (Warmup) 
## Chain 4 Iteration:  800 / 4000 [ 20%]  (Warmup) 
## Chain 3 Iteration:  900 / 4000 [ 22%]  (Warmup) 
## Chain 2 Iteration:  800 / 4000 [ 20%]  (Warmup) 
## Chain 4 Iteration:  900 / 4000 [ 22%]  (Warmup) 
## Chain 1 Iteration:  500 / 4000 [ 12%]  (Warmup) 
## Chain 4 Iteration: 1000 / 4000 [ 25%]  (Warmup) 
## Chain 3 Iteration: 1000 / 4000 [ 25%]  (Warmup) 
## Chain 2 Iteration:  900 / 4000 [ 22%]  (Warmup) 
## Chain 4 Iteration: 1100 / 4000 [ 27%]  (Warmup) 
## Chain 1 Iteration:  600 / 4000 [ 15%]  (Warmup) 
## Chain 2 Iteration: 1000 / 4000 [ 25%]  (Warmup) 
## Chain 4 Iteration: 1200 / 4000 [ 30%]  (Warmup) 
## Chain 3 Iteration: 1100 / 4000 [ 27%]  (Warmup) 
## Chain 2 Iteration: 1100 / 4000 [ 27%]  (Warmup) 
## Chain 1 Iteration:  700 / 4000 [ 17%]  (Warmup) 
## Chain 4 Iteration: 1300 / 4000 [ 32%]  (Warmup) 
## Chain 2 Iteration: 1200 / 4000 [ 30%]  (Warmup) 
## Chain 4 Iteration: 1400 / 4000 [ 35%]  (Warmup) 
## Chain 3 Iteration: 1200 / 4000 [ 30%]  (Warmup) 
## Chain 1 Iteration:  800 / 4000 [ 20%]  (Warmup) 
## Chain 2 Iteration: 1300 / 4000 [ 32%]  (Warmup) 
## Chain 4 Iteration: 1500 / 4000 [ 37%]  (Warmup) 
## Chain 2 Iteration: 1400 / 4000 [ 35%]  (Warmup) 
## Chain 3 Iteration: 1300 / 4000 [ 32%]  (Warmup) 
## Chain 4 Iteration: 1600 / 4000 [ 40%]  (Warmup) 
## Chain 4 Iteration: 1700 / 4000 [ 42%]  (Warmup) 
## Chain 2 Iteration: 1500 / 4000 [ 37%]  (Warmup) 
## Chain 1 Iteration:  900 / 4000 [ 22%]  (Warmup) 
## Chain 3 Iteration: 1400 / 4000 [ 35%]  (Warmup) 
## Chain 4 Iteration: 1800 / 4000 [ 45%]  (Warmup) 
## Chain 2 Iteration: 1600 / 4000 [ 40%]  (Warmup) 
## Chain 4 Iteration: 1900 / 4000 [ 47%]  (Warmup) 
## Chain 1 Iteration: 1000 / 4000 [ 25%]  (Warmup) 
## Chain 3 Iteration: 1500 / 4000 [ 37%]  (Warmup) 
## Chain 2 Iteration: 1700 / 4000 [ 42%]  (Warmup) 
## Chain 4 Iteration: 2000 / 4000 [ 50%]  (Warmup) 
## Chain 4 Iteration: 2001 / 4000 [ 50%]  (Sampling) 
## Chain 1 Iteration: 1100 / 4000 [ 27%]  (Warmup) 
## Chain 3 Iteration: 1600 / 4000 [ 40%]  (Warmup) 
## Chain 2 Iteration: 1800 / 4000 [ 45%]  (Warmup) 
## Chain 4 Iteration: 2100 / 4000 [ 52%]  (Sampling) 
## Chain 1 Iteration: 1200 / 4000 [ 30%]  (Warmup) 
## Chain 2 Iteration: 1900 / 4000 [ 47%]  (Warmup) 
## Chain 3 Iteration: 1700 / 4000 [ 42%]  (Warmup) 
## Chain 1 Iteration: 1300 / 4000 [ 32%]  (Warmup) 
## Chain 4 Iteration: 2200 / 4000 [ 55%]  (Sampling) 
## Chain 2 Iteration: 2000 / 4000 [ 50%]  (Warmup) 
## Chain 2 Iteration: 2001 / 4000 [ 50%]  (Sampling) 
## Chain 3 Iteration: 1800 / 4000 [ 45%]  (Warmup) 
## Chain 1 Iteration: 1400 / 4000 [ 35%]  (Warmup) 
## Chain 4 Iteration: 2300 / 4000 [ 57%]  (Sampling) 
## Chain 2 Iteration: 2100 / 4000 [ 52%]  (Sampling) 
## Chain 3 Iteration: 1900 / 4000 [ 47%]  (Warmup) 
## Chain 1 Iteration: 1500 / 4000 [ 37%]  (Warmup) 
## Chain 4 Iteration: 2400 / 4000 [ 60%]  (Sampling) 
## Chain 2 Iteration: 2200 / 4000 [ 55%]  (Sampling) 
## Chain 1 Iteration: 1600 / 4000 [ 40%]  (Warmup) 
## Chain 4 Iteration: 2500 / 4000 [ 62%]  (Sampling) 
## Chain 2 Iteration: 2300 / 4000 [ 57%]  (Sampling) 
## Chain 3 Iteration: 2000 / 4000 [ 50%]  (Warmup) 
## Chain 3 Iteration: 2001 / 4000 [ 50%]  (Sampling) 
## Chain 1 Iteration: 1700 / 4000 [ 42%]  (Warmup) 
## Chain 4 Iteration: 2600 / 4000 [ 65%]  (Sampling) 
## Chain 2 Iteration: 2400 / 4000 [ 60%]  (Sampling) 
## Chain 1 Iteration: 1800 / 4000 [ 45%]  (Warmup) 
## Chain 3 Iteration: 2100 / 4000 [ 52%]  (Sampling) 
## Chain 4 Iteration: 2700 / 4000 [ 67%]  (Sampling) 
## Chain 2 Iteration: 2500 / 4000 [ 62%]  (Sampling) 
## Chain 1 Iteration: 1900 / 4000 [ 47%]  (Warmup) 
## Chain 4 Iteration: 2800 / 4000 [ 70%]  (Sampling) 
## Chain 3 Iteration: 2200 / 4000 [ 55%]  (Sampling) 
## Chain 2 Iteration: 2600 / 4000 [ 65%]  (Sampling) 
## Chain 4 Iteration: 2900 / 4000 [ 72%]  (Sampling) 
## Chain 1 Iteration: 2000 / 4000 [ 50%]  (Warmup) 
## Chain 1 Iteration: 2001 / 4000 [ 50%]  (Sampling) 
## Chain 2 Iteration: 2700 / 4000 [ 67%]  (Sampling) 
## Chain 3 Iteration: 2300 / 4000 [ 57%]  (Sampling) 
## Chain 4 Iteration: 3000 / 4000 [ 75%]  (Sampling) 
## Chain 1 Iteration: 2100 / 4000 [ 52%]  (Sampling) 
## Chain 2 Iteration: 2800 / 4000 [ 70%]  (Sampling) 
## Chain 4 Iteration: 3100 / 4000 [ 77%]  (Sampling) 
## Chain 3 Iteration: 2400 / 4000 [ 60%]  (Sampling) 
## Chain 1 Iteration: 2200 / 4000 [ 55%]  (Sampling) 
## Chain 2 Iteration: 2900 / 4000 [ 72%]  (Sampling) 
## Chain 4 Iteration: 3200 / 4000 [ 80%]  (Sampling) 
## Chain 3 Iteration: 2500 / 4000 [ 62%]  (Sampling) 
## Chain 1 Iteration: 2300 / 4000 [ 57%]  (Sampling) 
## Chain 2 Iteration: 3000 / 4000 [ 75%]  (Sampling) 
## Chain 4 Iteration: 3300 / 4000 [ 82%]  (Sampling) 
## Chain 2 Iteration: 3100 / 4000 [ 77%]  (Sampling) 
## Chain 3 Iteration: 2600 / 4000 [ 65%]  (Sampling) 
## Chain 1 Iteration: 2400 / 4000 [ 60%]  (Sampling) 
## Chain 4 Iteration: 3400 / 4000 [ 85%]  (Sampling) 
## Chain 2 Iteration: 3200 / 4000 [ 80%]  (Sampling) 
## Chain 3 Iteration: 2700 / 4000 [ 67%]  (Sampling) 
## Chain 1 Iteration: 2500 / 4000 [ 62%]  (Sampling) 
## Chain 4 Iteration: 3500 / 4000 [ 87%]  (Sampling) 
## Chain 2 Iteration: 3300 / 4000 [ 82%]  (Sampling) 
## Chain 3 Iteration: 2800 / 4000 [ 70%]  (Sampling) 
## Chain 1 Iteration: 2600 / 4000 [ 65%]  (Sampling) 
## Chain 4 Iteration: 3600 / 4000 [ 90%]  (Sampling) 
## Chain 2 Iteration: 3400 / 4000 [ 85%]  (Sampling) 
## Chain 1 Iteration: 2700 / 4000 [ 67%]  (Sampling) 
## Chain 3 Iteration: 2900 / 4000 [ 72%]  (Sampling) 
## Chain 4 Iteration: 3700 / 4000 [ 92%]  (Sampling) 
## Chain 2 Iteration: 3500 / 4000 [ 87%]  (Sampling) 
## Chain 1 Iteration: 2800 / 4000 [ 70%]  (Sampling) 
## Chain 4 Iteration: 3800 / 4000 [ 95%]  (Sampling) 
## Chain 3 Iteration: 3000 / 4000 [ 75%]  (Sampling) 
## Chain 2 Iteration: 3600 / 4000 [ 90%]  (Sampling) 
## Chain 1 Iteration: 2900 / 4000 [ 72%]  (Sampling) 
## Chain 4 Iteration: 3900 / 4000 [ 97%]  (Sampling) 
## Chain 2 Iteration: 3700 / 4000 [ 92%]  (Sampling) 
## Chain 3 Iteration: 3100 / 4000 [ 77%]  (Sampling) 
## Chain 1 Iteration: 3000 / 4000 [ 75%]  (Sampling) 
## Chain 4 Iteration: 4000 / 4000 [100%]  (Sampling) 
## Chain 4 finished in 237.3 seconds.
## Chain 2 Iteration: 3800 / 4000 [ 95%]  (Sampling) 
## Chain 3 Iteration: 3200 / 4000 [ 80%]  (Sampling) 
## Chain 1 Iteration: 3100 / 4000 [ 77%]  (Sampling) 
## Chain 2 Iteration: 3900 / 4000 [ 97%]  (Sampling) 
## Chain 1 Iteration: 3200 / 4000 [ 80%]  (Sampling) 
## Chain 3 Iteration: 3300 / 4000 [ 82%]  (Sampling) 
## Chain 2 Iteration: 4000 / 4000 [100%]  (Sampling) 
## Chain 2 finished in 252.6 seconds.
## Chain 1 Iteration: 3300 / 4000 [ 82%]  (Sampling) 
## Chain 3 Iteration: 3400 / 4000 [ 85%]  (Sampling) 
## Chain 1 Iteration: 3400 / 4000 [ 85%]  (Sampling) 
## Chain 3 Iteration: 3500 / 4000 [ 87%]  (Sampling) 
## Chain 1 Iteration: 3500 / 4000 [ 87%]  (Sampling) 
## Chain 3 Iteration: 3600 / 4000 [ 90%]  (Sampling) 
## Chain 1 Iteration: 3600 / 4000 [ 90%]  (Sampling) 
## Chain 3 Iteration: 3700 / 4000 [ 92%]  (Sampling) 
## Chain 1 Iteration: 3700 / 4000 [ 92%]  (Sampling) 
## Chain 3 Iteration: 3800 / 4000 [ 95%]  (Sampling) 
## Chain 1 Iteration: 3800 / 4000 [ 95%]  (Sampling) 
## Chain 3 Iteration: 3900 / 4000 [ 97%]  (Sampling) 
## Chain 1 Iteration: 3900 / 4000 [ 97%]  (Sampling) 
## Chain 3 Iteration: 4000 / 4000 [100%]  (Sampling) 
## Chain 3 finished in 300.5 seconds.
## Chain 1 Iteration: 4000 / 4000 [100%]  (Sampling) 
## Chain 1 finished in 300.9 seconds.
## 
## All 4 chains finished successfully.
## Mean chain execution time: 272.8 seconds.
## Total execution time: 301.1 seconds.

Lets look at the parameter outputs. First the main effects.

#precis(m10me)
plot(precis(m10me))

## 144 vector or matrix parameters hidden. Use depth=2 to show them.

#hetergenity amongs grids in stones
plot(precis(m10me , depth=3 , pars="a_grid"))

Tree density has a reliable positive impact on the probability of using tools, whereas stone abundance has a small, unreliable positive impact on tool use. There is a weak interaction effect as well- places where there are more .

post <- extract.samples(m10me)
str(post)

## List of 12
##  $ a_bar      : num [1:8000, 1] 2.47 2.47 2.52 2.53 2.68 ...
##  $ a_grid     : num [1:8000, 1:40] -1.69 -1.79 -1.39 -1.65 -2.55 ...
##  $ sigma_stone: num [1:8000, 1] 1.33 1.14 1.15 1.23 1.43 ...
##  $ z_id       : num [1:8000, 1:4, 1:17] 0.154 -1.301 -1.353 -1.242 -0.328 ...
##  $ bPTxS      : num [1:8000, 1] -0.00251 -0.00142 -0.06499 0.02509 0.07459 ...
##  $ bPT        : num [1:8000, 1] 0.606 0.773 0.748 0.696 0.661 ...
##  $ bS         : num [1:8000, 1] 0.018 0.096 0.1518 0.1415 -0.0304 ...
##  $ ap         : num [1:8000, 1] -1.33 -1.24 -1.24 -1.17 -1.37 ...
##  $ sigma_id   : num [1:8000, 1:4] 0.816 0.47 0.477 0.524 0.735 ...
##  $ L_Rho_id   : num [1:8000, 1:4, 1:4] 1 1 1 1 1 1 1 1 1 1 ...
##  $ a_id       : num [1:8000, 1:17, 1:4] 0.126 -0.612 -0.645 -0.651 -0.241 ...
##  $ Rho_id     : num [1:8000, 1:4, 1:4] 1 1 1 1 1 1 1 1 1 1 ...
##  - attr(*, "source")= chr "ulam posterior from object"

p_link_palm <- function(x){
    scapula <- mean(post$a_grid)
    id <- 1
    logit_scale <- with(post , ap + a_id[,id,1]*0 +  (bS + a_id[,id,2])*scapula +
      (bPT + a_id[,id,3]*0)*x + (bPTxS + a_id[,id,4]*0)*scapula*x )
    return(logistic(logit_scale))
}

palm_seq <-  seq(from=min(data_list_daily$count_palm_std) , 
                 to=max(data_list_daily$count_palm_std) , length=30)

p_raw <- sapply( palm_seq, function(x) p_link_palm(x) )

plot(data_list_daily$nutcrackin ~ data_list_daily$count_palm_std ,
     pch=19 , col=col.alpha("green4",0.004), ylab="probability of nut cracking",
     xlab= "palm tree density/ 22 m^2 grid (standardized)")

pred_median <- apply(p_raw , 2 , median)
lines(pred_median ~ palm_seq , lw=2, col=1 , lty=1)

for (j in sample( c(1:2000) , 100) ){
  lines( p_raw[j,] ~ palm_seq , lw=3, col=col.alpha("green4", alpha=0.1) , lty=1)
}

We can also plot predictions of varying effects for all 17 individuals who used tools. One of them does not like using tools.

## per id plot
plot(data_list_daily$nutcrackin ~ data_list_daily$count_palm_std ,
     pch=19 , col=col.alpha("green4",0.004), ylab="probability of nut cracking",
     xlab= "palm tree density/ 22 m^2 grid (standardized)")

#lines(pred_median ~ palm_seq , lw=2, col=1 , lty=1)

for ( i in 1:max(data_list_daily$id)){
  dpred <- list(
    id=rep(i,30), #list of ones we will replace
    #log_avg_stone_std=rep(median(post$a_bar),30),
    count_palm_std=palm_seq,
    stone_grid_index=rep(1,30),
    grid_id_follow=rep(1,30)
  )
  link2 <- link(m10me, data=dpred , replace=list(stone_grid_index=a_grid_s_z , grid_id_follow=a_grid_f_z) )
  pred_median <- apply(link2$p , 2 , median)
  lines(pred_median ~ palm_seq , lw=2, col=col.alpha("green4",0.5) , lty=1)
}

Stone Availabilty

post <- extract.samples(m10me)
str(post)

## List of 12
##  $ a_bar      : num [1:8000, 1] 2.47 2.47 2.52 2.53 2.68 ...
##  $ a_grid     : num [1:8000, 1:40] -1.69 -1.79 -1.39 -1.65 -2.55 ...
##  $ sigma_stone: num [1:8000, 1] 1.33 1.14 1.15 1.23 1.43 ...
##  $ z_id       : num [1:8000, 1:4, 1:17] 0.154 -1.301 -1.353 -1.242 -0.328 ...
##  $ bPTxS      : num [1:8000, 1] -0.00251 -0.00142 -0.06499 0.02509 0.07459 ...
##  $ bPT        : num [1:8000, 1] 0.606 0.773 0.748 0.696 0.661 ...
##  $ bS         : num [1:8000, 1] 0.018 0.096 0.1518 0.1415 -0.0304 ...
##  $ ap         : num [1:8000, 1] -1.33 -1.24 -1.24 -1.17 -1.37 ...
##  $ sigma_id   : num [1:8000, 1:4] 0.816 0.47 0.477 0.524 0.735 ...
##  $ L_Rho_id   : num [1:8000, 1:4, 1:4] 1 1 1 1 1 1 1 1 1 1 ...
##  $ a_id       : num [1:8000, 1:17, 1:4] 0.126 -0.612 -0.645 -0.651 -0.241 ...
##  $ Rho_id     : num [1:8000, 1:4, 1:4] 1 1 1 1 1 1 1 1 1 1 ...
##  - attr(*, "source")= chr "ulam posterior from object"

p_link_stone <- function(x){
    id <- 1
    logit_scale <- with(post , ap + a_id[,id,1]*0 +  (bS + a_id[,id,2])*x +
      (bPT + a_id[,id,3]*0)*0 + (bPTxS + a_id[,id,4]*0)*0*x )
    return(logistic(logit_scale))
}

stone_seq <-  seq(from=min(data_list_daily$log_avg_stone_std) , 
                 to=max(data_list_daily$log_avg_stone_std) , length=30)

p_raw <- sapply( stone_seq, function(x) p_link_stone(x) )

plot(data_list_daily$nutcrackin ~ data_list_daily$log_avg_stone_std ,
     pch=19 , col=col.alpha("darkslateblue",0.004), ylab="probability of nut cracking",
     xlab= "log stone density/ 110 m^2 grid (standardized)")

pred_median <- apply(p_raw , 2 , median)
lines(pred_median ~ stone_seq , lw=2, col=1 , lty=1)

for (j in sample( c(1:2000) , 100) ){
  lines( p_raw[j,] ~ stone_seq , lw=3, col=col.alpha("darkslateblue", alpha=0.1) , lty=1)
}

There also be a weak interaction, but treat with caution.

##stone abundance
par( mfrow=c(1,3))
stone_samp <- c(-2,0,2)

for(j in 1:3){
  plot(data_list_daily$nutcrackin ~ data_list_daily$count_palm_std ,
       pch=19 , col=col.alpha("green4",0.004), ylab="probability of nut cracking",
       xlab= "palm tree density/ 22 m^2 grid (standardized)" , main=stone_samp[j] )

  palm_seq <-  seq(from=min(data_list_daily$count_palm_std) ,
                   to=max(data_list_daily$count_palm_std) , length=30)
  dpred <- list(
    id=rep(1,30), #list of ones we will replace
    log_avg_stone_std=rep(stone_samp[j],30),
    count_palm_std=palm_seq,
    stone_grid_index=rep(1,30),
    grid_id_follow=rep(1,30)
  )

  link2 <- link(m10me, data=dpred , replace=list(id=a_id_z , stone_grid_index=a_grid_s_z , grid_id_follow=a_grid_f_z) )
  pred_median <- apply(link2$p , 2 , median)
  lines(pred_median ~ palm_seq , lw=2, col=1 , lty=1)

  for (j in sample( c(1:2000) , 100) ){
    lines( link2$p[j,] ~ palm_seq , lw=3, col=col.alpha("green4", alpha=0.1) , lty=1)
  }
}

#dev.off()

Terrestriality

m_h2 <- ulam(
  alist(
    height_dm ~ dzipois( p , lambda ),
    logit(p) <- ap + a_id[id,1] + (bNp + a_id[id,3])*nutcrackin ,
    log(lambda) <- al + a_id[id,2] + (bNl + a_id[id,4])*nutcrackin ,
    # adaptive priors - non-centered
    transpars> matrix[id,4]:a_id <-
      compose_noncentered( sigma_id , L_Rho_id , z_id ),
    matrix[4,id]:z_id ~ normal( 0 , 1 ),
    # fixed priors
    c(ap,bNp,bNl) ~ dnorm( 0 , 1 ),
    al ~ dnorm( 3.5 , 2 ),
    vector[4]:sigma_id ~ dexp(1),
    cholesky_factor_corr[4]:L_Rho_id ~ lkj_corr_cholesky( 3 ),
    # compute ordinary correlation matrixes from Cholesky factors
    gq> matrix[4,4]:Rho_id <<- Chol_to_Corr(L_Rho_id)
  ) , data=data_list_height , chains=4 , cores=4 , cmdstan = TRUE)

## Running MCMC with 4 parallel chains, with 1 thread(s) per chain...
## 
## Chain 1 Iteration:   1 / 1000 [  0%]  (Warmup)

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 1 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 1

## Chain 2 Iteration:   1 / 1000 [  0%]  (Warmup)

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[4] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[4] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 2 Exception: lkj_corr_cholesky_lpdf: Random variable[4] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 2

## Chain 3 Iteration:   1 / 1000 [  0%]  (Warmup)

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[4] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 3 Exception: lkj_corr_cholesky_lpdf: Random variable[4] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 3

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Iteration:   1 / 1000 [  0%]  (Warmup)

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[2] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

## Chain 4 Exception: lkj_corr_cholesky_lpdf: Random variable[3] is 0, but must be positive! (in '/tmp/RtmpAd2AVf/model-c2f548499100.stan', line 25, column 4 to column 38)

## Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,

## Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.

## Chain 4

## Chain 1 Iteration: 100 / 1000 [ 10%]  (Warmup) 
## Chain 4 Iteration: 100 / 1000 [ 10%]  (Warmup) 
## Chain 3 Iteration: 100 / 1000 [ 10%]  (Warmup) 
## Chain 2 Iteration: 100 / 1000 [ 10%]  (Warmup) 
## Chain 1 Iteration: 200 / 1000 [ 20%]  (Warmup) 
## Chain 3 Iteration: 200 / 1000 [ 20%]  (Warmup) 
## Chain 2 Iteration: 200 / 1000 [ 20%]  (Warmup) 
## Chain 4 Iteration: 200 / 1000 [ 20%]  (Warmup) 
## Chain 1 Iteration: 300 / 1000 [ 30%]  (Warmup) 
## Chain 2 Iteration: 300 / 1000 [ 30%]  (Warmup) 
## Chain 3 Iteration: 300 / 1000 [ 30%]  (Warmup) 
## Chain 1 Iteration: 400 / 1000 [ 40%]  (Warmup) 
## Chain 4 Iteration: 300 / 1000 [ 30%]  (Warmup) 
## Chain 2 Iteration: 400 / 1000 [ 40%]  (Warmup) 
## Chain 3 Iteration: 400 / 1000 [ 40%]  (Warmup) 
## Chain 1 Iteration: 500 / 1000 [ 50%]  (Warmup) 
## Chain 1 Iteration: 501 / 1000 [ 50%]  (Sampling) 
## Chain 4 Iteration: 400 / 1000 [ 40%]  (Warmup) 
## Chain 2 Iteration: 500 / 1000 [ 50%]  (Warmup) 
## Chain 2 Iteration: 501 / 1000 [ 50%]  (Sampling) 
## Chain 1 Iteration: 600 / 1000 [ 60%]  (Sampling) 
## Chain 3 Iteration: 500 / 1000 [ 50%]  (Warmup) 
## Chain 3 Iteration: 501 / 1000 [ 50%]  (Sampling) 
## Chain 2 Iteration: 600 / 1000 [ 60%]  (Sampling) 
## Chain 4 Iteration: 500 / 1000 [ 50%]  (Warmup) 
## Chain 4 Iteration: 501 / 1000 [ 50%]  (Sampling) 
## Chain 1 Iteration: 700 / 1000 [ 70%]  (Sampling) 
## Chain 2 Iteration: 700 / 1000 [ 70%]  (Sampling) 
## Chain 1 Iteration: 800 / 1000 [ 80%]  (Sampling) 
## Chain 4 Iteration: 600 / 1000 [ 60%]  (Sampling) 
## Chain 3 Iteration: 600 / 1000 [ 60%]  (Sampling) 
## Chain 2 Iteration: 800 / 1000 [ 80%]  (Sampling) 
## Chain 1 Iteration: 900 / 1000 [ 90%]  (Sampling) 
## Chain 2 Iteration: 900 / 1000 [ 90%]  (Sampling) 
## Chain 1 Iteration: 1000 / 1000 [100%]  (Sampling) 
## Chain 1 finished in 1769.5 seconds.
## Chain 2 Iteration: 1000 / 1000 [100%]  (Sampling) 
## Chain 2 finished in 1860.2 seconds.
## Chain 4 Iteration: 700 / 1000 [ 70%]  (Sampling) 
## Chain 3 Iteration: 700 / 1000 [ 70%]  (Sampling) 
## Chain 4 Iteration: 800 / 1000 [ 80%]  (Sampling) 
## Chain 3 Iteration: 800 / 1000 [ 80%]  (Sampling) 
## Chain 3 Iteration: 900 / 1000 [ 90%]  (Sampling) 
## Chain 4 Iteration: 900 / 1000 [ 90%]  (Sampling) 
## Chain 3 Iteration: 1000 / 1000 [100%]  (Sampling) 
## Chain 3 finished in 2844.4 seconds.
## Chain 4 Iteration: 1000 / 1000 [100%]  (Sampling) 
## Chain 4 finished in 3053.2 seconds.
## 
## All 4 chains finished successfully.
## Mean chain execution time: 2381.8 seconds.
## Total execution time: 3053.7 seconds.

## Warning: 6 of 2000 (0.0%) transitions hit the maximum treedepth limit of 10.
## See https://mc-stan.org/misc/warnings for details.

plot(precis( m_h2 , depth=2))

## 168 matrix parameters hidden. Use depth=3 to show them.

precis( m_h2 , depth=2)

## 168 matrix parameters hidden. Use depth=3 to show them.

##                   mean         sd        5.5%      94.5%     rhat  ess_bulk
## bNl         -0.7481725 0.08967661 -0.89094817 -0.6063615 1.002843  798.2844
## bNp          1.1878297 0.14180814  0.95764220  1.4083081 1.002752 1030.5424
## ap          -2.3930813 0.13605202 -2.59388330 -2.1783546 1.007757  610.8038
## al           4.1783673 0.02957207  4.13421340  4.2240747 1.009969  565.9312
## sigma_id[1]  0.5163979 0.10217924  0.37901208  0.6919352 1.005957  713.7998
## sigma_id[2]  0.1205353 0.02323810  0.09008362  0.1606623 1.006809  701.4872
## sigma_id[3]  0.4916765 0.11387326  0.33270949  0.6959382 1.001755 1077.1723
## sigma_id[4]  0.3306998 0.07481651  0.23149843  0.4657552 1.001728  970.4360

precis( m_h2 , depth=3 , pars="Rho_id")

##                     mean        sd       5.5%       94.5%      rhat  ess_bulk
## Rho_id[1,1]  1.000000000 0.0000000  1.0000000  1.00000000        NA        NA
## Rho_id[2,1] -0.434492558 0.1901663 -0.7016454 -0.09527151 1.0020829  929.3918
## Rho_id[3,1] -0.420023675 0.2088108 -0.7197414 -0.06584689 0.9990519 1663.1131
## Rho_id[4,1] -0.191375372 0.2201639 -0.5342442  0.16532271 1.0038083  968.7778
## Rho_id[1,2] -0.434492558 0.1901663 -0.7016454 -0.09527151 1.0020829  929.3918
## Rho_id[2,2]  1.000000000 0.0000000  1.0000000  1.00000000        NA        NA
## Rho_id[3,2]  0.252294131 0.2168762 -0.1204801  0.57163875 0.9998656 1875.1295
## Rho_id[4,2]  0.004964414 0.2124145 -0.3322853  0.33817939 1.0016527 1015.1019
## Rho_id[1,3] -0.420023675 0.2088108 -0.7197414 -0.06584689 0.9990519 1663.1131
## Rho_id[2,3]  0.252294131 0.2168762 -0.1204801  0.57163875 0.9998656 1875.1295
## Rho_id[3,3]  1.000000000 0.0000000  1.0000000  1.00000000        NA        NA
## Rho_id[4,3] -0.029169033 0.2590645 -0.4565290  0.38869499 1.0026738  778.8528
## Rho_id[1,4] -0.191375372 0.2201639 -0.5342442  0.16532271 1.0038083  968.7778
## Rho_id[2,4]  0.004964414 0.2124145 -0.3322853  0.33817939 1.0016527 1015.1019
## Rho_id[3,4] -0.029169033 0.2590645 -0.4565290  0.38869499 1.0026738  778.8528
## Rho_id[4,4]  1.000000000 0.0000000  1.0000000  1.00000000        NA        NA

Let plot the probability of being terrestrial in each context with got plots for each individual. Unsurprisingly, they are more terrestrial when using tools.

post <- extract.samples(m_h2)

dens(logistic(post$ap) , xlim=c(0.05, 0.5 ) , xlab="probability of being terrestrial")
dens(logistic(post$ap + post$bNp) , add=TRUE , col="slateblue" )
legend(x = "topright", legend = c("tool use", "non tool use") , fill = c("slateblue","black") , bty='n' ) 
blog=1.5
for(i in 1:17){
  squanch <- logistic(post$ap + post$a_id[,i,1] )
  points( median(squanch) , (i-.1)/blog , pch=18)
  segments(x0=HPDI(squanch)[1] , x1=HPDI(squanch)[2] , y0=(i-.1)/blog , y1=(i-.1)/blog  )
  squanch <- logistic(post$ap + post$a_id[,i,1]  + post$bNp + post$a_id[,i,2])
  points( median(squanch) , (i+.1)/blog , col="slateblue" , pch=16)
  segments(x0=HPDI(squanch)[1] , x1=HPDI(squanch)[2] , y0=(i+.1)/blog , y1=(i+.1)/blog , col="slateblue" )
}

Ok now we can plot the heights in decimeters (Sorry). Same story. Note 50 is 5 m.

dens( (1-logistic(post$ap))*exp(post$al) , xlim=c(0, 200) , xlab="height in dm during follows" , show.HPDI=.99999 )
dens((1-logistic(post$ap + post$bNp))*exp(post$al + post$bNl) , add=TRUE , col="slateblue" , show.HPDI=.99999)
legend(x = "topright", legend = c("tool use", "non tool use") , fill = c("slateblue","black") , bty='n' ) 
blog=200
for(i in 1:17){
  squanch <- (1-logistic(post$ap + post$a_id[,i,1] ))*exp(post$al+ post$a_id[,i,3])
  points( median(squanch) , (i-.1)/blog , pch=18)
  segments(x0=HPDI(squanch)[1] , x1=HPDI(squanch)[2] , y0=(i-.1)/blog , y1=(i-.1)/blog  )
  squanch <- (1-logistic(post$ap + post$a_id[,i,1]  + post$bNp + post$a_id[,i,2]))*exp(post$al + post$a_id[,i,3]+ post$bNl + post$a_id[,i,4])
  points( median(squanch) , (i+.1)/blog , col="slateblue" , pch=16)
  segments(x0=HPDI(squanch)[1] , x1=HPDI(squanch)[2] , y0=(i+.1)/blog , y1=(i+.1)/blog , col="slateblue" )
}

Predictive maps per grid cell,

One of Tati’s big questions was, does the relationship between terrestriality out of tool use context, and terrestriality within tool use context differ? So if we are trying to predict terrestriality rates inside and outside of tool use context, are the the same within a quadrat.